CN107480340A - A kind of multiple dimensioned loading spectrum method for building up based on EMD Time-frequency Analysis - Google Patents
A kind of multiple dimensioned loading spectrum method for building up based on EMD Time-frequency Analysis Download PDFInfo
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Abstract
The invention belongs to fatigue reliability technical field, and a kind of multiple dimensioned loading spectrum method for building up based on EMD Time-frequency Analysis is disclosed, comprised the following steps：1) stationarity and ergodic inspection are carried out to load history；2) EMD is carried out to load history to decompose to obtain IMF components；3) Hilbert conversion is carried out to each IMF components to determine the frequency band of each IMF components；4) the load amplitude probability density function of each IMF components is obtained；5) hypothesis testing is carried out, obtained each load amplitude probability density function is the loading spectrum on corresponding frequency band.Load history data are decomposed and loading spectrum are established on different frequency bands by this method, avoid the load that will be born and be considered as the drawbacks of permanent width or variable amplitude loading of only one frequency establishes loading spectrum, the multiple dimensioned loading spectrum established using this method can provide more accurate foundation for the Calculation of Fatigue Life and Analysis on Fatigue Reliability of component of machine.
Description
Technical field
The invention belongs to fatigue reliability technical field, more particularly, to a kind of multiple dimensioned loading spectrum method for building up.
Background technology
《The research that the effect of double frequency load influences on fatigue properties》In, research finds the master of many engineering structures such as bridge
Some main parts sizes of beam, aircraft and automobile etc., the load born be by multiple different frequencies and amplitude load into
Divide and formed.The document is directed to the double frequency load being made up of the cyclic loading of two different frequencies, have studied and is gone through by complex load
Fatigue properties of the Cheng Zuoyong mechanical component under the effect of double frequency load, result of the test and single-frequency load condition are carried out
Compare.As a result show, under double frequency load test, the estimation of fatigue life of sample is closer actual.
《The research of Fatigue Design Method for Francis Turbine Runner》In, ground by substantial amounts of data statistic analysis with experiment
Study carefully, obtained the loading spectrum and material property parameter required for francis turbine runner fatigue design.Establishing that three frequencies are dynamic should
Power superposition mechanical model, and in material property testing, carried out the research of frequency influence and multifrequency overlaying influence.But this article
The split-band for offering the not loading spectrum to multifrequency load-time history is established and furtherd investigate, and in fact, different frequency bands
Influence of the load to fatigue life and fatigue reliability is different.So, it should further investigate and provide multifrequency load-time
The method for building up of the loading spectrum split-band of course.
《The research of Prediction method for fatigue life under the non-same frequency load of multiaxis》In, same frequency load effect lower member non-to multiaxis
Stress analyzed.The characteristics of non-ess-strain loaded with frequency in lower material plane of multiaxis changes over time is have studied,
It was found that the non-same change for loading lower material plane upper stress strain frequently is luffing, non-same phase and is periodic, build simultaneously
The fatigue life prediction model of correlation is found.But the method for building up of the document same frequency loading spectrum not non-to multiaxis gos deep into
Research, and loading spectrum is the key technology of research mechanical Parts life-span and fatigue reliability, therefore tackle non-same frequency and carry
The foundation of lotus spectrum carries out detailed analysis and further investigation.
Each document is analyzed for its loading problem in each studying above, not the load to surveying or emulating
Lotus-time history carries out the further investigation in frequency domain, is not known when real load is made up of multiple frequency bands, loading spectrum is built
Cube method.And actual load-time history is made up of the load contribution of several different frequencies and amplitude mostly.If will
These complex load histories are simplified to single-frequency situation to establish its loading spectrum, then can have a tremendous difference with actual conditions,
And then larger error can be produced with Analysis on Fatigue Reliability to the estimation of fatigue life carried out according to loading spectrum.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides a kind of based on EMD Time-frequency Analysis
Multiple dimensioned loading spectrum method for building up, it is possible to achieve to the load of various components of machine (i.e. multiple time chis on different frequency bands
On degree) establish loading spectrum.The load-time history of actual measurement or emulation for each component of machine, will using EMD decomposition methods
Load-time history data are transformed on the different frequency bands of different time scales, are realized to the load-time history in different frequencies
The foundation of the multiple dimensioned loading spectrum taken.
To achieve the above object, it is proposed, according to the invention, provide a kind of multiple dimensioned loading spectrum based on EMD Time-frequency Analysis and build
Cube method, it is characterised in that comprise the following steps：
1) load-time history data are carried out with stationary test and ergodic inspection, to determine the load-time
Course data are steady and ergodic；
2) EMD decomposition is carried out to load-time history data, to obtain the IMF time domain components of different frequency bands；
3) Hilbert conversion is carried out to each IMF time domains component, obtains the Hilbert marginal spectrums of each IMF time domains component, from
And determine the frequency band corresponding to each IMF time domains component；
4) data statistics is carried out respectively to the load cycle amplitude in IMF time domains component corresponding to each frequency band, be then fitted
Load amplitude probability density distribution, obtain the load amplitude probability density function of IMF time domains component corresponding to each frequency band；
5) hypothesis testing is carried out to each load amplitude probability density function respectively, each load amplitude probability is close obtained from
It is the loading spectrum on corresponding frequency band to spend function, and then obtains the loading spectrum on multiple frequency bands, i.e., the load in multiple time scales
Spectrum.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show
Beneficial effect：
This method decomposes load-time history data the foundation that loading spectrum is carried out on different frequency bands, avoids routine
The load born or stress are considered as the drawbacks of permanent width or variable amplitude loading of only one frequency establishes loading spectrum, application by method
The multiple dimensioned loading spectrum that this method is established can provide more for the Calculation of Fatigue Life and Analysis on Fatigue Reliability of component of machine
For accurate foundation.
Brief description of the drawings
Fig. 1 is the load-time history of the main cutting force in embodiment 1；
Fig. 2 a~Fig. 2 j are each IMF components that the main cutting force signal of embodiment 1 decomposes to obtain through EMD respectively, wherein horizontal
Axle represents the time, and unit is the second；
Fig. 3 is the Hilbert marginal spectrums of the main cutting force signal of embodiment 1；
Fig. 4 a~Fig. 4 g are the Hilbert marginal spectrums of each IMF components of main cutting force signal of embodiment 1；
Fig. 5 a~Fig. 5 g are the load amplitude distribution histograms of each IMF components of main cutting force signal of embodiment 1；
Fig. 6 is the load-time history of the total lifting force of ship lift of embodiment 2；
Fig. 7 a~Fig. 7 i are each IMF components that the total lifting force of ship lift of embodiment 2 decomposes to obtain through EMD；
Fig. 8 is that the ship lift of embodiment 2 always lifts the Hilbert marginal spectrums of force signal；
Fig. 9 a~Fig. 9 d are that the ship lift of embodiment 2 always lifts the Hilbert marginal spectrums of each IMF components of force signal；
Figure 10 a~Figure 10 d are that the ship lift of embodiment 2 always lifts the load amplitude distribution column of each IMF components of force signal
Figure；
Figure 11 is the flow chart of this method.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below
Conflict can is not formed each other to be mutually combined.
Embodiment 1
The present embodiment is related to a kind of foundation of the multiple dimensioned cutting force spectrum of vertical machining centre.
Milling Force test experiments are carried out on TC500 vertical drilling-tappings center.Experiment is surveyed from Kistler9257B types three-dimensional
Power instrument and 5017B type multichannel charge amplifiers.Three-dimensional force tester is arranged on workbench in experiment, and workpiece is fixed
On dynamometer, the cutting force of machining center can be measured.Experiment parameter is as shown in table 1.
Because the most cutting operating modes of the vertical machining centre are milling operating mode, milling cutter is slotting cutter.Here, with cutter
The multiple dimensioned loading spectrum of cutting force is carried out for slotting cutter, exemplified by cutting parameter milling operating mode as shown in table 1 to establish.
The TC500 Milling Forces of table 1 test machined parameters
(1) main cutting force FcLoad-time history
The load-time history of the main cutting force measured according to experiment, as shown in Figure 1.
(2) to surveying main cutting force FcSignal carry out stationarity and it is ergodic examine, to determine that the load signal is
It is steady and ergodic.
If load-time history meets stationarity and ergodic theorem, can just be replaced with arbitrary sample overall.Therefore load
Stationarity and ergodic theorem be establishment loading spectrum necessary condition.In engineering stationarity is carried out frequently with runs test method
Examine.
Here by main cutting force sample size 10000, using runs test method, sample is divided into 25 sections, each
Interval Sampling point 400, the then mean-square value of computation interval, and study the wheel number of mean-square value dispersion degree, number r is taken turns here
=13, fall in (8,18) region, so receiving stationarity hypothesis under level of significance α=0.05.
Each state process is difficult to directly examine, and rule of thumb, the stationary random signal run into common engineering can
Regard ergodic as.Therefore it is stable to demonstrate main cutting force sample, you can effectively thinks that total physical efficiency of sample expires
Sufficient stationarity and ergodic theorem.
(3) EMD decomposition is carried out to main cutting force, obtains the IMF components of different frequency bands, as shown in Figure 2.
EMD methods realize the decomposition of IMF functions by screening process, obtained successively by screening process signal from high frequency to
Multiple IMF components C of low frequencynAnd discrepance r (t)n, until meeting previously given end condition, then screening process terminates.Most
Eventually, primary signal can be expressed as shown in formula (1)：
In formula, each IMF components C1(t),C2(t),…,Cn(t) represent primary signal from high frequency to n frequency range of low frequency respectively
Composition.
Here screening process is constrained using imitative Cauchy's test for convergence (as shown in formula (2)).
In formula, SD is referred to as sieving threshold value, typically takes 0.2-0.3；T is the time span of signal sequence；h1k(t) it is kth
Secondary screening the data obtained；h1(k-1)(t) it is -1 screening the data obtained of kth, t is the time.
(4) Hilbert conversion is carried out to main cutting force signal, obtains the Hilbert marginal spectrums of main cutting force signal, such as schemed
Shown in 3.
By defining the yellow spectrum of Hilbert, as shown in formula (3).
In formula, ai(t) it is amplitude, ωi(t) it is instantaneous frequency, the number of IMF components is n.
Further definable marginal spectrum, as shown in formula (4).
In formula, h (ω) is Hilbert marginal spectrums, and T is the time span of signal sequence.Hilbert limits profiling is
The rule that the amplitude of signal changes and changed with frequency, is capable of the amplitude of each frequency content of accurate description, while have very high
Resolution ratio.
(5) Hilbert conversion is carried out to each IMF components of main cutting force signal, obtains the Hilbert sides of each IMF components
Border compose (as shown in Figure 4), to determine the load frequency band residing for each component, as the load for judging different frequency bands for dynamic force still
The foundation of static force, the load relatively low to frequency can be considered static force.
The frequency of the 8th rank IMF components is very low it can be seen from the marginal spectrum of 8 order components before IMF decomposition in Fig. 4,
The 9th rank IMF components and later each order component can be regarded as static force；And the maximum amplitude of the 8th rank IMF components is 6.3N, only
For the 25.2% of main cutting force average 25N.So only consider that amplitude and the of a relatively high preceding 7 rank IMF components of frequency are established here
Loading spectrum.
(6) its load cycle and cycle count method are determined respectively to the IMF component signals of each frequency band.Here, will be vertical
Brill attacks every turn of central principal axis and is once used as a load cycle, and main shaft number of revolutions is corresponding load cycle times N, such as formula
(5) shown in.
In formula, L is length of cut, unit mm；F is the amount of feeding, unit mm/r.
(7) it is fitted the probability density function of load cycle amplitude in each IMF components.Data system is carried out to each IMF components
Meter analysis, parameter Estimation and hypothesis testing.Here, the load amplitude distribution histogram of each IMF components is obtained, as shown in Figure 5.It is right
Block diagram is more complicated to be fitted using Gaussian mixtures or mixed-weibull distribution etc..
(8) the load amplitude distribution obtained to fitting carries out χ2Examine.Through examining, each IMF component amplitudes of main cutting force
Probability density function corresponds with different parameter distributions, obeys null hypothesis.The probability density letter of each IMF components load amplitude
Number is as shown in formula (6)-(12).
Embodiment 2
The present embodiment is related to a kind of foundation of the multiple dimensioned loading spectrum of ship lift gear.
The fail-safe analysis of ship lift gear, fatigue life test are required for gear load spectrum to be used as basic foundation.In order to
The statistical nature of gear dynamic load in practical work process is disclosed, the present invention provides the specific gear load for being easy to application
Compose method for building up.
Except gear material in itself and lubrication etc. is in addition to condition of work, several failure modes of gear during working gear with engaging
Used load size and certain time internal load the effect number of moment is relevant.The purpose for establishing gear load spectrum is that announcement
This magnitude of load and the statistical nature for acting on number.This statistical law is grasped, will be to analyzing ship lift gear fatigue life
And fatigue reliability provides important evidence.
(1) ship lift gear load-time history
Tested due to failing load during to ship lift actual motion, here according to gear teeth meshing moment corresponding outer load
The corresponding statistical law of lotus, gear total lifting force F within certain working time load is provided using Monte Carlo emulation modes
Lotus-time history.
Analyzed so that ship lift travels at the uniform speed the load that stage gear is subject to as an example：
Include in the load that the stage ship lift gear that travels at the uniform speed is subject to：Uneven weight F1, wind load F2And frictional force
F3, then total lifting force be
F=F1+F2+F3 (13)
According to the statistical analysis to each load progress in formula (13), using Monte Carlo emulation modes to ship lift
The maximum load that every turn of gear is once subject to is sampled, and obtains load-time history when gear travels at the uniform speed, as Fig. 6 shows.
(2) stationarity and ergodic inspection are carried out to total lifting force signal of emulation, to determine that the dummy load is believed
Number it is steady and ergodic.
Here the total lifting force sample size 10000 of ship lift is chosen, using runs test method, sample is divided into 25 areas
Between, each Interval Sampling point 400, the then mean-square value of computation interval, and calculate the wheel number of mean-square value dispersion degree, here
Number r=11 is taken turns, is fallen in (8,18) region, so receiving stationarity hypothesis under level of significance α=0.05.
Each state process is difficult to directly examine, and rule of thumb, the stationary random signal run into common engineering can
Regard ergodic as.Therefore it is stable to demonstrate total lifting force sample, you can effectively thinks that total physical efficiency of sample expires
Sufficient stationarity and ergodic theorem.
(3) EMD decomposition is carried out to the total lifting force of ship lift, obtains IMF components (the circular reference of different frequency bands
Embodiment 1), as shown in Figure 7.
(4) Hilbert conversion is carried out to the total lifting force of ship lift, obtains Hilbert marginal spectrums (the specific meter of total lifting force
Calculation method is with reference to embodiment 1), as shown in Figure 8.
(5) Hilbert conversion is carried out to each IMF components of the total lifting force of ship lift, obtains the Hilbert of each IMF components
Marginal spectrum (as shown in Figure 9), to determine the load frequency band residing for each component.As the load for judging different frequency bands for dynamic force also
It is the foundation of static force, the load relatively low to frequency can be considered static force.
The frequency of the 4th rank IMF components is very low it can be seen from the marginal spectrum of 4 order components before IMF decomposition in Fig. 9,
So can by the 5th rank IMF components and later each order component regard static force as, here only it is higher to frequency before 4 rank IMF components
Establish loading spectrum.
(6) load cycle counting is carried out using amplitude method here.
Data statistics, data fitting and parameter Estimation are carried out respectively to the IMF components load amplitude of each frequency band.
(7) it is fitted the probability density function of load amplitude in each IMF components.Each IMF components load amplitude is distributed column
Figure is as shown in Figure 10.More complicated to block diagram can use Gaussian mixtures or mixed-weibull distribution etc. to intend
Close.
(8) the load amplitude distribution obtained to fitting carries out χ2Examine.Through examining, each IMF components of the total lifting force of ship lift
The probability density function of load amplitude corresponds with different parameter distributions, obeys null hypothesis.Each IMF components load amplitude
Shown in probability density function such as formula (14)-(17).
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included
Within protection scope of the present invention.
Claims (1)
1. a kind of multiple dimensioned loading spectrum method for building up based on EMD Time-frequency Analysis, it is characterised in that comprise the following steps：
1) load-time history data are carried out with stationary test and ergodic inspection, to determine the load-time history
Data are steady and ergodic；
2) EMD decomposition is carried out to load-time history data, to obtain the IMF time domain components of different frequency bands；
3) Hilbert conversion is carried out to each IMF time domains component, obtains the Hilbert marginal spectrums of each IMF time domains component, so as to really
Frequency band corresponding to fixed each IMF time domains component；
4) data statistics is carried out respectively to the load cycle amplitude in IMF time domains component corresponding to each frequency band, is then fitted load
Amplitude probability density is distributed, and obtains the load amplitude probability density function of IMF time domains component corresponding to each frequency band；
5) hypothesis testing, each load amplitude probability density letter obtained from are carried out to each load amplitude probability density function respectively
Number is the loading spectrum on corresponding frequency band, and then obtains the loading spectrum on multiple frequency bands, i.e., the loading spectrum in multiple time scales.
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| CN113095192A (en) * | 2021-04-02 | 2021-07-09 | 中国农业大学 | Dynamic load spectrum compiling method based on time domain extrapolation technology |
| CN114034492A (en) * | 2021-11-03 | 2022-02-11 | 交通运输部公路科学研究所 | Automobile part load spectrum rapid compression method based on Hilbert-Huang transform |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111597722A (en) * | 2020-05-20 | 2020-08-28 | 北京航空航天大学 | Method for predicting equipment precision retention time by using running state information |
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| CN113095192A (en) * | 2021-04-02 | 2021-07-09 | 中国农业大学 | Dynamic load spectrum compiling method based on time domain extrapolation technology |
| CN113095192B (en) * | 2021-04-02 | 2023-12-12 | 中国农业大学 | Dynamic load spectrum compiling method based on time domain extrapolation technology |
| CN114034492A (en) * | 2021-11-03 | 2022-02-11 | 交通运输部公路科学研究所 | Automobile part load spectrum rapid compression method based on Hilbert-Huang transform |
| CN114034492B (en) * | 2021-11-03 | 2024-04-05 | 交通运输部公路科学研究所 | Hilbert-Huang transform-based rapid compression method for load spectrum of automobile part |
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